You can check the ssl and tls prefs on the about:config page. You can open the about:config page via the location bar.

• http://kb.mozillazine.org/about:config

If any ssl or tls pref is bold (user set) then right-click that pref and choose "Reset" to reset the pref to the default value. Paste this regular expression (include the slashes) in the Search bar at the top of the about:config page:

• /security.*ssl|security.*tls/

Did that aleady. Reset all to default - did not solve it. Also enabled all - did not solve it.

And when you reset FF it resets all those to default as well.

I thought that it's my router, but Chrome and IE work just fine.

You can check the connection settings.

• Tools > Options > Advanced > Network : Connection > Settings
• https://support.mozilla.org/kb/Options+window+-+Advanced+panel

If you do not need to use a proxy to connect to internet then try to select "No Proxy" if "Use the system proxy settings" or one of the others do not work properly.

See "Firefox connection settings":

• https://support.mozilla.org/kb/Firefox+cannot+load+websites+but+other+programs+can

No proxy used as well :(

Boot the computer in Windows Safe Mode with network support (press F8 on the boot screen) as a test.

• http://www.bleepingcomputer.com/tutorials/how-to-start-windows-in-safe-mode/

Do a malware check with several malware scanning programs on the Windows computer. Please scan with all programs because each program detects different malware. All these programs have free versions.

Make sure that you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender:
  http://windows.microsoft.com/en-us/windows/using-defender
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked
• https://support.mozilla.org/kb/troubleshoot-firefox-issues-caused-malware